Word-to-Symbol Translation (AF 402, AF 502)

Some phrases translate in the order you hear them. 'Three times a number, decreased by five' really is 3x - 5, left to right. But 'five less than three times a number' does not. 'Less than' tells you something is being taken away from a quantity named earlier in the sentence, even though it's spoken first. The number getting reduced is '3 times a number', and 5 comes off it: 3x - 5. Read it backwards in your head — 'less than' always points back at what comes after it in the sentence.

Work clause by clause. Find the unknown and name it x. Find the operations in the order they act on x, not the order of English words: a 'times' word gives multiplication, 'more than' or 'increased by' gives addition, 'less than' or 'decreased by' subtracts from the thing already built, and 'quotient of A and B' always means A divided by B, A on top. Build the expression piece by piece, then if the sentence says two things 'equal' each other, set the two expressions equal and you have an equation ready to solve by collecting x terms on one side.

This topic is the entry point for every other function-building skill on this strand. Once you can turn a sentence into an equation, you're set up to read a graph as the same story in picture form, or to decide whether a situation grows by adding (linear), multiplying (exponential), or dividing (inverse). Every one of those skills starts with translating words into an accurate symbolic rule.